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Unformatted text preview: Bayesian Image Super-Resolution Michael E. Tipping and Christopher M. Bishop Microsoft Research, Cambridge, U.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Published as: “Bayesian image super-resolution.” In S. Becker, S. Thrun, and K. Obermayer (Eds.), Advances in Neural Information Processing Systems 15. MIT Press. Year of publication: 2003 This version typeset: June 26, 2006 Available from: http://www.miketipping.com/papers.htm Correspondence: email@example.com Abstract The extraction of a single high-quality image from a set of low-resolution images is an im- portant problem which arises in fields such as remote sensing, surveillance, medical imaging and the extraction of still images from video. Typical approaches are based on the use of cross-correlation to register the images followed by the inversion of the transformation from the unknown high resolution image to the observed low resolution images, using regu- larization to resolve the ill-posed nature of the inversion process. In this paper we develop a Bayesian treatment of the super-resolution problem in which the likelihood function for the image registration parameters is based on a marginalization over the unknown high- resolution image. This approach allows us to estimate the unknown point spread function, and is rendered tractable through the introduction of a Gaussian process prior over im- ages. Results indicate a significant improvement over techniques based on MAP (maximum a-posteriori) point optimization of the high resolution image and associated registration parameters. 1 Introduction The task in super-resolution is to combine a set of low resolution images of the same scene in order to obtain a single image of higher resolution. Provided the individual low resolution images have sub-pixel displacements relative to each other, it is possible to extract high frequency details of the scene well beyond the Nyquist limit of the individual source images. Ideally the low resolution images would differ only through small (sub-pixel) translations, and would be otherwise identical. In practice, the transformations may be more substantial and involve rotations or more complex geometric distortions. In addition the scene itself may change, for instance if the source images are successive frames in a video sequence. Here we focus attention on static scenes in which the transformations relating the source images correspond to translations and rotations, such as can be obtained by taking several images in succession using a hand held digital camera. Our approach is readily extended to more general projective transformations if desired....
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